Let's recalled I kind of main issue 1 if you wanna keep your forces separate from your acceleration but the main thing will be focusing on this Situated in this section is cases were a 0 is constant and you're given it For the aid given by centripetal acceleration Bridger move in inner circle are now on the poor side were mostly of Forest Focus on Sanchez pushing and pulling weight and then argue contact forces normal for says and friction there 1 forests That we will deal with the classes not In this less that I did just because we deal that at a later chapter will we do energy And that is the 1st judo spraying So does keep that in mind that down the road you will have to add additional forced to less what we're going to focus on Tuesday Are problems that involve Essentially every problem will always have some of these and wait will almost always be there could be very rarely do anything in outer space but but Conceptual talent is dealing with friction so that is today Iowa will focus on Friday Is how they handle the triple acceleration and the conceptual challenge that will be dealing with And all of these problems is the fact that there's almost always going to be some sort of any quality the ramp to know when to treat as inequality and what I mean by That I mean they're really be dealing with things like maximum minimum and just to do so Maximum to movement among to move maximum onto that movement will not move were just the start will be the use of the phrase is worded abusing the figure out what is that People usually it's a 0 but not always and learning how to deal with these phrases and the hazards of the situation Is what will be working up to a final peace and all of this is that we almost always have to deal with components and the twister adding now as we really wanna choose a smart scored system so that is Kind of overview of the problems will be dealing with this week She er Any questions Not before we start the problems I have a couple demonstrations will be doing 1st I don't win quicker questions with them this time is 1 show you some of the behavior that's associated with friction and a concept of just moving better be important during these problems The idea organ and highlighting In these demonstrations is the following that the source of friction 2 pieces 1 which is static friction Which has this feature that I can change inside its given by a less than or equal to MEI there is kinetic friction values cases we have a coefficient of friction that you will be either give are half the for dozen the main relations were going to be looking at and how does it basically works out we have are handy dandy little boats from

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End We have our people actually means cars against cars carts and they're on a surface I read a poem The guy's is how much force Does it take to pull them a lot so We need massive these as 5 kilograms each so it's 10 kilograms stroll right so we wait

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Of these is that by gravity and G so we've got basically a 100 new sitting in here that we're trying you see on my still of the Force reportable and right now

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Fully with 10 militants and they're not moving at all going with 5 new examiner will meet I 15 And they're not moving I could even go up to 20 and they won't so there's lots of forces I could pull away And they want a bipolar more than 20 they start moving at It's really hard to say you want it I get a little bit about 20 11 Oak employ opening them and then while when did it start to move now it will be a little more obvious this 1 is a smooth start the otherwise the next mini usurious has sandpaper paper under it

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So now noticed a mail at 238 35 Cards foreign and duties 68 and that a move and notice how much is Job is down once slight it goes always the 70 John Denver 55 when it's like so what is happening here

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They would have an idea what We were demonstrating with them so I hadn't objects on a table And I'm pulling It propped up So the job down as the static for 2 and the been higher than maximum static version is higher than the characters why was it not moving until I reach song to a level What I want you to do here is my blocked artery drew their drive again me joy just a block I want you to make a free body diagram for this block that I just pulled make a free body diagram and then I lied we will have a quitter question event how many forces you end up with senior free body diagram Excellent almost you have for I'll curious to see what you're missing if you have 3 what are the floor and this particular problem they wanna give me some less Where a force of fractured I'm uses diagrams of by force of friction is going backwards what else do we have the normal force that was not what else do we have gravity and all that the fault gravity and the fault so People and The just out of curiosity shot at which forced you were missing most your resume normal exhibits said Fritz remember any due out into contact was always the normal force that's always there Now there is a fairly straightforward 1 we make it XUY corn system we like each direction separately and in this case for the y direction Monday's we know a 0 it doesn't accelerate up-or-down because it never gets any vertical velocity so a wider 0 So at normal minors At W. equal 0 so I know my normal force is Because I plug-in here for F. W Now what hold them of about whether by luck in the x direction and initially a x 0 so what that tells me is as poorly in mind ever That has people 0 so my polling forest has people might force of friction which I know is less than 3 quantum U.S. times and which is not changing and that is this whole piece of the beginning Park where I start was some very small I do not accelerated off because the force of friction Is allowed to cancel that and that is the key thing here this force of correction Is able to cancel out whatever polling I apply until I reach my maximum then it will ever once it moves whether I am accelerating or constant velocity I now have to use kinetic friction but in this case it starts the blue with velocity and direction the constant once a movie so I still have an 80 x equals 0 but for a different reason It's now moving at Can't speak now my have P minus F have still equal 0 F equals might force of friction but now it's kinetic friction and so Eagleton UK at hand and the general rule is that you can say is I was always a alas then U.S. anew on know this from your everyday experience if you put that anything right once you get it going It's easier to keep it going but it usually is to get started at best as a consequence of kinetic friction is almost always last The static 13 If you have to move I device object once you get it moving it's easier to keep it that is our 1st which we see something changing and then you agree to limit 20 questions on that yes GDP So Momentum is something we will talk about the context of forces in a later chapter So you don't need a finesse it if you if you think of those germs and helps to assure what's going on and that's fine Other questions so now let's see it in another context

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A common thing that have Is a rap So I said were building up the pieces and often things are moving enable wife because we like to ski like to snowboard to job motorcycles elected jump we drive on hills above any other started we like to build pyramids were injured Egyptians so

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It almost anything we do often a ramp comes in I want things to keep in mind which will really get into more detail later should acidity and is where comes the forces its velocity most object people cars by roller skaters arrows bullets a baseball

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Is advocates week intrigue as a small little block will be called particle so we got is boring problems of plots and inclined planes and ramps

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They look like they have no connection to reality is unless still located not really sliding blocks down an inclined plane and Einar I know when a 3-year-old other toys down the stairs The Paris Maya trend provider is looking how they off fall the matter which 1 and with falls baleful the same as that We wanted develop here everything acts the same And so we just treat all like a block anything that At an angle is a ramp so what happens right is you start to tilt your ramp

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And not as a dozen mode Think about Vlasic request were due comedy forces erected is it not because not accelerate as tho accelerators that accelerated amid some key points so it has an acceleration of slides down the ramp

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But And so bad as other type of notice a just move problem there was A maximum angle But with it Would not slight And all these cases

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But that's a math problems right it were looking for the maximum angle True not slide were really doing were gonna be using the fact that static friction of the change forests and fine the case were forced A static Equal to that of the remake it any bigger static friction can get Any bigger and now boasts life so we solve for the point just before Anything happens which means 2 things in this case were both using an acceleration still 0 even tho it's about have acceleration and we're taking the maximum of that defined the place Where that's just about the change from not being 0 now 1 thing I can do write a Islamist sandpaper says got higher coefficient of friction

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So I guess drew much higher wrangle

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And a tip over civic and get it North cheaper but the mass like that A good too much our angle before starts a slide that they're just like 5 and making a for not That is because new S Is much bigger So the maximum force of is much bigger so

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This trend Counteract bigger and bigger forces and will see that The problems we do any questions on their back to remind lots and lots of injured and as I said A Monday variations in which something like this and they were doing Inclined planes so that it could be a ladder against a wall when as the latter gorgeous like it to be on you know you your friends building appear amid rumors of new slide off so there's lots of ways this 4th of friction come into things but it's all the same basic concept and use the same techniques Vick Napa algebra would be slightly different from problem the problem so wet Go to our 1st problem now that their 1st quicker question theory of this is the standard black arrested an inclined plane forms angle 38 degrees the horizontal white forests is required to hold

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What's worse is required of hold The block in place Ross talk about what force is required to accelerate the block and renew it with without friction that this would never be an exam problem like that exactly 4 problems on Lazio use want 4 times right so this is for different problems in here But it gives me a chance to do for them because they're all basically exactly the same problem What we do is you are different facts and information about force effect of At least to equate with force of Richard is something you have to become very comfortable with now the other thing you have become very comfortable with In physics is choosing your according system so when a start this problem before I even knew the problem Let's try the picture for the problem

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Now 1 thing you Madam noticed were there any numbers given due in this problem Which what I acceleration also gave an angle I didn't else I'd be amassed 30 the other stuff So there is a good idea because recent afraid to order the part I'm going to do this Problem variables just so you can see the structure of it and not numbers and most of the forest problems it really is a great advantage to you if you only like members the because 1 of things it often happens for instance I just noticed Man not always But often cancels right because you've got an energy for gravity and you got an in the sector locked So a lot of time if you if you don't get comfortable doing it with variables A notice would once cancel out You will not realize that you actually have enough information so upon my connected to the mass and 1 number for answering alike the Cassidy the that You're used to plug it an earlier and if you do the algebra you'll see a cancels so with Forest problems I really encourage you to do it the way the examples in class and Jibril variables and then you get used to that point number 1 point number 2 were always going to be looking at our components map occasionally only 1 of the 2 directions will matter so we will need you lose both components but were always everything's almost always in a be to and the question is how we draw court system and you have often were the 1 choice South For instance hair I draw cordoned system with an extra taxes like that notice what I've done is my X axis is parallel to The ramp end I could also dropped a normal X Y axis here the key Aspect of this is BY axis Based Parallel to gravity So if I just look at the 3 basic forces That I would be drawing for this block let's not think about the problem right now this is about a block sitting on a ramp no friction I would have weighed down notice the normal forces always perpendicular to the surface so it's off at an angle and of the right to make forces notice They might to coordinate systems 1 of these has to be broken and the components of I use this court and sister weight Is already in the wider access because it was the gravity and be normal force We'll have to Combine best I use the best forward and system then gravity gets broken into 2 components be normal force is already in The Y direction so Depending on what's going on and the problem is 1 of these 2 reported systems Will be easier to use Roughly 80 per cent of the time you will find myself the series using this quarter sister while we mostly uses Foreign system because most of the time if I look at the acceleration in this quarantine system equal 0 and X equals something maybe 0 maybe not but we very rarely have the block coming off the ramp in this court and sister a X and a Y will both have to be broken and the components A is along ramp that it just turns out It's easier and usually nicer The deal with the accelerator Only in 1 direction and know that it's always 0 another they have the to accelerate so this is a common court system will you What that means is you will have the most often break Wakenda into components Band You wanna be very comfortable drawing your triangles so here is the direction of the wait here is my angle theta At Chiba me But the labels for weight down here But like added right from 18 and XOY quartered system like this here is the 2 components I need so I need to know this angle in here is 90 miners later Because it makes a right angle that's a right angle So the angle in here is now faded and so this becomes FW data And this becomes FW signed said again trade and geometry are the key and this has the aligned breaking the components that I really Suggest 3 choices for this a cover up all the time 1 might be the memorize it too might be great faith In your ability it always do the geometry and the 3rd is to keep in mind important trek A ramp has the angle of Xerox which direction is gravity Straight down so And which direction is the x axis of my angle is fate is 0 horizontal with disappears when data is 0 But sign 0 0 0 Because what we call physics about sort of checking our answer does it make sense if make compounded parallel to my ramp along my ran a better be 0 broken my ramping 0 And sign a 0 0 coastline is not 1 so you could always when you write it down use that sort of Mathematical idea the check psilosis 3 things that you gotta memorize with going on is geometry or you can use That intuition if you memorize know the formula has to do with that angle every now and then that's not being you're given to get a worry that a little bit Any questions on that Stop there Yes the At that Why it right I know what I'm saying is my lamp was completely flat Not at the main also favor 0 then this 1 has to disappear because when I'm on a flat ground like this that is only going down along the rapper Libya to do my ramp right when the ramp 0 gravity is all perpendicular the ramp don't have an angle the gravity has a component along the ramp and perpendicular to the rim So that You know which 1 of these will disappear The normal course is always perpendicular to the surface So the angle abide by use of right the masses they are perpendicular righted easy say the normal forces always parallel to left to right now straight up right now that this angle and Mike wanted system is perpendicular to the Is And parallel to the surface the normal course will be my wife direction and will see that the problem that we saw that I pick it up quarantine system such is my normal XOY the gravity is always in wider And the normal force Picks up components of its now So the normal force phone it yet right direction and this is where the line gets a little confusing because whether I pick Mike

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Warning system at this angle or at this angle I still contacts in like and that language is a little confusing so what is my XOY component 1st I have to pick my quarantine system then I get to decide if I pick this quarter and sister knows my normal force has components but This forward meant Its gravity that has components But You'll see it as we do a lot of examples as you practice them alive with 1 discussion section you get a practice for there's a ramp A now But is it any more questions III I did say were still only using basically 1 concept was With the combined but it is getting much deeper there's a lot more to that concept so I agree it is kind of order now so let's go back to our question why force is required to just hold the block in place and this case We're going to ignore friction will do that when 1st so We got our replica question End But would ask ourselves how many forces Erna our free body diagram so Were and have a blot on our inclined plane that that some angle there's no and this has written sewed staying on loan from there's to reduce lighting town so I've the placed the price you're asking is what forces required to hold it in place what fire started work right Ah yes I use this same 1 for every 1 of these big ones like I'm being very elicited one's life role for questions one's life the good request When where when I when I posed a lecture world will try and make it clear How many were in each 1 the first one at 4 0 that 56 per cent of us went with rate at the very good start and I'll tell you right now in some way ways if you miss back Wednesday and the rest of the problem becomes impossible So visitors once you've gotta get that question right so we got our block its itinerary inclined playing our free body diagram is way down normal force Perpendicular of plane at our force appalling holding it in place because gravity pull down now known as I drew my free body diagram of all forces coming from the center that is not unique you can also draw this way Yeah sometimes because that's where the force point is pushing up on that have I also like to draw blocked up a lot of people like notice on the master of the edges of a dot that you draw the forces from an international physics there really looking at it this version is like to draw map We wanted to be just a place where the figure recorded system we know therefore that our acceleration is going to be 0 so in some sense for acceleration factor it won't matter which 1 we do per cent but What we do know is accelerates at all the acceleration is along the surface so because of that I'm going to pick an X otherwise parallel to my surface and you need to draw this returned the problem you need to draw your free body diagram and you do not draw your acceleration on your free body diagram it is not a force is acceleration where you should indicate somewhere to yourself so you don't forget what the acceleration of the 3 pieces that you need event once you have this picture was and write down your equations and the 2 directions in this case we will have to break Gravity and components so we won't have W. cosine there and F. W but yes signed data that banned in our y direction and wise positive up so the normal is positive VFW cosigned is negative peoples and a sub y but a civilized 0 and Yanks direction are pushing is positive We have a minus F W signed later egos and a acts and we wanna know when that would be 0 So we see that the force we need to push where it is just the way signed vendor Which would be Ng science data So we would need another mass and the angle We were given the 30 if I wanted the number here I would need to know the maps so that is the minimum or the foresight of force was just Holden placed notice by breaking in the components I immediately see from my ex direction that F miners FW signed later People's and a acts of F P is greater than FW signed trader A X is greater than 0 and accelerate up The ramp FP is less than FW signed but X is less than 0 And I go down the the ramp so I'm like the case of friction is not like there's a range of pushing I use that it will move and there's a maximum value that he huge replaced with no friction that accelerates either up the ramp were down the ramp unless I hold it with exactly the right course 1 of them albeit with exactly the right course Managers stays there were no acceleration of it a little less gravity wins slide down a little bit more I win and I pushed it up So I can use that's right away to answer the 2nd question how much must 1st be for a At The . 5 meters 4 seconds were right so I wonder the 2nd part of the question I just plug in a equals . 5 meters per 2nd squared and I solve for FP as the other advantage of leaders variables to the end of the question does happen asked 2 different things You don't have to really it you can just plug in your numbers you've done right we solve the general problem and now we just plug whatever numbers they ask you for different mass Wedel I have to do You just plug and for that matter So any Quentin's I non friction case death But remember that the wait is 1 of the forces we have a formula for the way it is always given by AMG so I'm just plugging end for the wait here get that question And I could do that right here as well I just haven't bothered to do it At a questions Excellent so now Were announced the question The same question But with friction so we ask our co-occur questioned

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Family Forces erected on the block now Won't very quick Bermuda like 30 seconds comedy forces around the block Where Now we're doing exactly this problem on big pussy Nana and there's how much like to push on it so it doesn't slide But there's friction enemy cuisine in the black And excellent before we just added that too so it was 3 before now it's for Now harder question What direction this fortune act so let me remind you are draw the picture here right we haven't inclined playing for a block on it Where again pledged was unnecessary force so that the bloc A mail Does not slide which direction is fortune acting Most of you went with downed the plane that is incorrect now let me ask you that's let's suppose I ask the question She Which direction as fortune acting now and that wardrobe quickly not as much confidence But now it is correct You you most areas which the right answer And here's what's going on and there is what makes a challenging there's too moments at which I'm not in a move the forest Cost to my mouse right It is what forces required the whole black in place Or holding the block advice was so if that's what I'm doing drawn all the block in place then But a lot is attempting to move down And should always opposes that attempt to move So Correction will be out and it helped me that means I need less forestall the place that I might be 0 4 how much force I need whole that locked in place so dozens slight 0 As just sitting there is not sliding friction is doing all the work for me and thereby put up here day I now need some the place but I need less force that there was no friction because friction is still helping me death I wanna push it up the ramp Now what did motion up the ramp so now which direction is down so I tried a push Up losing new direction for friction it goes down so the way works by what my free body diagram for the 1st case I have that friction and pushing going up the ramp notice Normal doesn't change Wake doesn't change that my wife the wide Directions is the same As before that hasn't changed we have a new act direction Corporation where we have we might News W sign say that that's the component of the weight and for this case we give a positive push and a positive force of friction Aris said that MAX which is 0 now that means The pushing force we need the magnitude of it Just These besides data minors Our force of friction and be maximum value for the will set the minimum value For further and how do we get the maximum value for the source of friction and this is the static friction case we Use the equal sign here and make the source of friction equal to the U. S F and which we solved using our y direction equation and back It is the central feature of all of these problems and so I'm just getting give you the answer now and then post As more detailed solution for you go from the Y direction we will get that the normal force is Ng cosigned data from the act direction we have a ready at there And we play again so the pooling forces Jim signed minus new Angie cosine now 1 last point the question asked us What we do what forces required to accelerate it better 3 meter . 3 meters per 2nd man this equation changes right The direction of F can is now Up I'm sorry is now down and so we change the minus sign here and we will have a S P B people Ng signed that I pull us mutate and So what I'm going to post for you know the details of this last and then 2nd problem is listed as a lecture problem I will probably post just as they attempted to capture video and tomorrow and class you're in a practice that is more discusses accident Friday we do circular motion